A man stnading in a swimming pool looks at a stone lying at the bottom. The depth of the swimming pool is h. At what distance from the surface of water is the image of the stone formed? (Line of vision is normal, Refractive index of water is n)

Options

A. h/n
B. n/h
C. h
D. hn

Answer

To solve the problem of finding the distance from the surface of the water at which the image of the stone is formed, we can use the concept of apparent depth in optics. The apparent depth can be calculated using the refractive index of the medium (water in this case).

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Depth of the swimming pool (h) = H
- Refractive index of water (n)

2. **Understand the Concept of Apparent Depth**:
- When light travels from a denser medium (water) to a less dense medium (air), the apparent depth (d') of an object submerged in the denser medium is given by the formula:
\[ d' = \frac{h}{n} \]
- Here, d' is the apparent depth, h is the actual depth of the object, and n is the refractive index of water.

3. **Calculate the Apparent Depth**:
- Substitute the values into the formula:
\[ d' = \frac{H}{n} \]
- This gives us the distance from the surface of the water to the image of the stone as seen by the man standing in the pool.

4. **Conclusion**:
- The distance from the surface of the water to the image of the stone is:
\[ d' = \frac{H}{n} \]

### Final Answer:
The image of the stone is formed at a distance of \(\frac{H}{n}\) from the surface of the water.

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